# Gauss

Senior Members

37

1. ## Can you do it in 20 words or less...

Evolution is the study of: Metamorphosis. Chaos Theory is the study of: Nonlinear dynamical and deterministic systems. Geography is the study of: Physical featues and resources. Physics is the study of: Interactions between matter and energy. Bio genetics is the study of: Genes in Living organisms. Done "19 words"
2. ## Can you do it in 20 words or less...

Evolution is the study of: Life gradually developing from the simple to the more complex. Chaos Theory is the study of: The behaviour of certain nonlinear dynamical systems and deterministic systems. Geography is the study of: The earth's physical featues, resources, climate and its population. Physics is the study of: The properties and interactions of matter and energy. Bio genetics is the study of: Living organisms and their genes.
3. ## Immortality?

No if's No but's I want to live forever
4. ## Quick LaTeX Tutorial

Dear Dave Thanks for the reply, I had a thought that might be the case. Regards Gauss
5. ## Ending the 0.999~ = 1 debates

Four points to consider First point: The proof simply states that x = 0.999... and the method used is smiliar to the one that is used to prove otherwise. The calculations are exact. Second point: Take another example: x = 3 Eq(1) 10*x = 10 * 3 Eq(2) Eq(2) - Eq(1) 9*x = 27 $x = \frac {27}{9}$ x = 3 Third Point: There is no reason whatsoever to use the formula for the sum of an infinite sequence in this case. I know the exact sum of: $S = \frac{9}{10} + \frac{9}{10^2} + \frac{9}{10^3} + ...$ Its $S = 0.\bar9$ However I would use the sum of an infinite sequence in the following case: $S_n = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ... + \frac{1}{2^n}$ Obviously, as $n \rightarrow \infty \mbox{\, } S_n \rightarrow 1$ Fourth point: This is the case for 2/9 x = 0.222... Eq (1) 10 * x = 10 * 0.222... x+x+x+x+x+x+x+x+x+x = 0.222... + 0.222... + 0.222... + 0.222... + 0.222... + 0.222... + 0.222... + 0.222... + 0.222... + 0.222... Eq(2) Eq (2) - Eq (1) x+x+x+x+x+x+x+x+x = 0.222... + 0.222... + 0.222... + 0.222... + 0.222... + 0.222... + 0.222... + 0.222... + 0.222... Eq(2) Since addition or multiplication is normally carried out from Right to Left and since this is an area of contention of what occurs or happens after the repeating dots (ellipses) then addition or multiplication in this instance is carried out from Left to Right. 9*x = 1.999... $x = \frac {1.999...}{9}$ $x = 0.222...}$
6. ## Quick LaTeX Tutorial

Dear Dave I have tried numerous times to use the latex code for Matrix and Align equations. When I use the command for matrix I get: $\begin{matrix} w & x \\ annoyed & z \end{matrix}$ and for align: \begin{align} w & x \\ annoyed & z \end{align} As you can see the ampersand persists. I have read a few 'latex' manuals and tried various code combinations. Could you or someone else be able to provide some information to overcome this problem. Regards Gauss
7. ## Ending the 0.999~ = 1 debates

x = 0.999... Eq (1) 10 * x = 10 * 0.999... x+x+x+x+x+x+x+x+x+x = 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... Eq(2) Eq (2) - Eq (1) x+x+x+x+x+x+x+x+x = 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... + 0.999... Since addition or multiplication is normally carried out from Right to Left and since this is an area of contention of what occurs or happens after the repeating dots (ellipses) then addition or multiplication in this instance is carried out from Left to Right. 9*x = 8.999... $x = \frac {8.999...}{9}$ $x = 0.999...$
8. ## Ending the 0.999~ = 1 debates

$0.\overline{0}1$ is another way of stating or trying to represent $\lim_{n\to\infty}10^{-n}$. Which is just an identity equation or equivalence statement. Dave's statement' date=' stated [math']0.\overline{0}1[/math] = 0
9. ## Ending the 0.999~ = 1 debates

This equation is not correct. All you have done is constructed a statement and stated the LHS equals the RHS.
10. ## Ending the 0.999~ = 1 debates

$1.\bar 0$ does not equal $0.\bar 9$ they are two distinct different numbers.
11. ## Ending the 0.999~ = 1 debates

1.\bar0 does not equal 0.\bar9 they are two distinct different numbers.
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